Open charm effects in the explanation of the long-standing “<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ρ</mml:mi><mml:mi>π</mml:mi></mml:math>puzzle”

Abstract

A detailed analysis of the open charm effects on the decays of $J/\ensuremath{\psi}({\ensuremath{\psi}}^{\ensuremath{'}})\ensuremath{\rightarrow}VP$ is presented, where $V$ stands for light vector meson and $P$ for light pseudoscalar meson. These are the channels that the so-called ``12% rule'' of perturbative QCD (pQCD) is obviously violated. Nevertheless, they are also the channels that violate the pQCD helicity selection rule at leading order. In this work, we put constraints on the electromagnetic contribution, short-distance contribution from the $c\overline{c}$ annihilation at the wave function origin, and long-distance contribution from the open charm threshold effects on these two decays. We show that interferences among these amplitudes, in particular, the destructive interferences between the short-distance and long-distance strong amplitudes, play a key role to evade the helicity selection rule and cause the significant deviations from the pQCD expected 12% rule.